Question

A box has a rectangular base with a length of 3x + 2 and width of 2x - 2, and the base has a perimeter of 60 centimeters. If the height of the box is x, what is the volume of the box?

Answer 1

The volume (v) of a box with a rectangular base, also known as a rectangular prism, is length×width×height:
v = l×w×h = lwh
Since we know the perimeter (p) is 60 cm, and perimeter (p) of a rectangle is twice the length plus twice the width:
p = 2l + 2w = 2(l+w)
60 = 2(3x+2+2x-2)
60 = 6x+4+4x-4 = 10x
10x = 60
x = 6 cm
So width (w) = 2x-2 = 2(6)-2 = 12-2 = 10 cm
and length (l) = 3x+2 = 3(6)+2 = 18+2 = 20 cm
Then back to our volume (v):
v = lwh = (20)(10)(6) = (200)(6)
$= 1200 \: {cm}^{3}$